In Latter-day Saint scripture, a revelation given to Enoch identifies God the Father as the "Man of Holiness" (Moses 6:57; Moses 7:35). Therefore, by LDS interpretation, when Christ says he is the Son of Man (capital M) he is saying he is the Son of God.
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SamuelJul 29 at 4:24

5 Answers
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Thus: “When E. Hiyya ben Adda died … R. Levi received his valuables. This was because his teacher used to say: ‘The disciple of bar nāšâ is as dear to him as his son.’ ” Here the expression plainly refers to the group of teachers

It is suggested that the idiom was used as a form of self-reference in cases where the speaker wished to show modesty or to speak of matters (such as his own death) which were distasteful—in any case in sayings where he wished to avoid speaking directly in the first person.
--Green, J. B., McKnight, S., & Marshall, I. H. (1992). Dictionary of Jesus and the Gospels (779). Downers Grove, Ill.: InterVarsity Press.

There are several theories about what Jesus was alluding to in calling himself son of Man (literally son of 'a-dam'):

A re-affimation of his authority to forgive sin (which entered via Adam).

An allusion to the suffering that he will undergo

A kindredness that will be evident at his return, in which he will come not just as a conqueror, but as a redeemer who is coming (back) to his own.

An allusion to his Messianic role, since the Messiah would be "the Son of Man"

A reference to the inheritor of the world, per Daniel 7. The last beast to have authority was "like a Son of Man"

With any of these motives, by speaking of himself in the third person, he is making an audacious claim (the power!) but couching it in the most humble terms he can.

He was alluding that he would fulfill the prophecy made by the Prophet Daniel in Daniel 7.

13 “In my vision at night I looked, and there before me was one like a
son of man,[a] coming with the clouds of heaven. He approached the
Ancient of Days and was led into his presence. 14 He was given
authority, glory and sovereign power; all nations and peoples of every
language worshiped him. His dominion is an everlasting dominion that
will not pass away, and his kingdom is one that will never be
destroyed.

It was as direct a claim of messiah ship a first century Jew could make. The Jews understood this and is why he was so widely held as a blasphemer by the Jewish people. This is further reiterated by passages like

I have heard that it is a mystery why Jesus referred to Himself as the Son of Man. And yet it was in fact what Jesus called Himself the most.

I see it like this, Jesus is speaking as God, because He is God. His perspective on everything is from the point of view of God. So what makes Jesus unique foremost, is not that He is a man who is God, but rather that He is God, but also a man. In all the Universe, here is God as "the Son of Man (mankind)". Or - I am God and also a man, not I am a man who is also God.

The major problem is that in the OT God clearly states that he is not a man. biblegateway.com/passage/…God is not a man, that he should lie; neither the son of man, that he should repent: hath he said, and shall he not do it? or hath he spoken, and shall he not make it good?
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public staticOct 20 '14 at 20:02

13 I saw in the night visions,
and behold, with the clouds of heaven
there came one like a son of man, and he came to the Ancient of Days
and was presented before him. 14 And to him was given dominion
and glory and kingdom, that all peoples, nations, and languages
should serve him; his dominion is an everlasting dominion,
which shall not pass away, and his kingdom one
that shall not be destroyed. — Daniel 7:13-14 RSV

Jesus refers to this when He is brought before the council, as described in Mark 14:

61b Again the high priest asked him, “Are you the Christ,
the Son of the Blessed?” 62 And Jesus said, “I am; and you
will see the Son of man seated at the right hand of Power, and coming
with the clouds of heaven. — Mark 14:61b-62 RSV

Then will appear the sign of the Son of Man in heaven. And then all the peoples of the earth will mourn when they see the Son of Man coming on the clouds of heaven, with power and great glory. — Matthew 24:30 NIV

I would say He referred to himself as "the son of man" to keep His identity a secret until it was the right time to die and let the Jews know He was the messiah. (as he did in Mark 14:61-64)
Not only is He the son of God, but He is too the son of Joseph. A man of flesh.
This going along with Hammer's answer on March 10 that He is speaking from God's point of view.

Jesus wanted to keep His identity secretive until the right and final moment.
Which is why He silenced the demons in Mark 1:34
and others in Matthew 8:3-4, 16:20 & 17:9 so that they would not say He was the son of God and He would be charged with Blasphemy.

Welcome to C.SE! When you get the chance, please check out our tour and specifically How we are different than other sites. This answer is a reasonable one to the question, but "I would say" makes it sound like personal opinion. If you could add references to others who say the same thing (and they do), it would help.
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Affable GeekFeb 18 '14 at 15:24